Progress in Traceable Nanoscale Capacitance Measurements Using Scanning Microwave Microscopy

Abstract

Reference samples are commonly used for the calibration and quantification of nanoscale electrical measurements of capacitances and dielectric constants in scanning microwave microscopy (SMM) and similar techniques. However, the traceability of these calibration samples is not established. In this work, we present a detailed investigation of most possible error sources that affect the uncertainty of capacitance measurements on the reference calibration samples. We establish a comprehensive uncertainty budget leading to a combined uncertainty of 3% in relative value (uncertainty given at one standard deviation) for capacitances ranging from 0.2 fF to 10 fF. This uncertainty level can be achieved even with the use of unshielded probes. We show that the weights of uncertainty sources vary with the values and dimensions of measured capacitances. Our work offers improvements on the classical calibration methods known in SMM and suggests possible new designs of reference standards for capacitance and dielectric traceable measurements. Experimental measurements are supported by numerical calculations of capacitances to reveal further paths for even higher improvements.

Traceable Nanoscale Measurements of High Dielectric Constant by Scanning Microwave Microscopy

“…The triplet capacitance standards are chosen on the thickest SiO 2 layer (4th plateau) of one reference sample. This reduces significantly the combined uncertainty level to 3% (k = 1) resulting from the depletion capacitance at the SiO 2 /Si interface as well as the observed parasitic series capacitances [32]. The error terms are found through a comparison between the measured SMM values and a thorough numerical modelling of the standard micro-capacitor structures (see Section 3.1).…”

“…The method applies the classical oneport VNA calibration using three known capacitance standards (triplet) to determine the three experimental error terms. These standards are established from reference capacitor triplet selected on the MC2 samples A61 or A64 [32]. The triplet capacitance standards are chosen on the thickest SiO 2 layer (4th plateau) of one reference sample.…”

“…These metal oxide semiconductor (MOS) capacitors are designed for capacitance values ranging from 200 aF to 10 fF [21]. We have recently reported on a comprehensive metrology characterization of these calibration samples [32], demonstrating a combined uncertainty of 3% at one standard deviation (k = 1) for capacitance measurements at the operating frequency of 3.6 GHz.…”

“…∆S 11,m corresponds to the difference between the raw S 11,m signals measured on individual capacitors C i and the S' 11,m signals measured on the dielectric layer surrounding the capacitor . This approach is intended to exclude the background capacitive signal, thus reducing stray capacitances involved in the measurement [32]. Moreover, the sample configuration is designed such that the investigated samples are placed in the immediate vicinity of the reference sample as previously reported in [29,32].…”

“…This approach is intended to exclude the background capacitive signal, thus reducing stray capacitances involved in the measurement [32]. Moreover, the sample configuration is designed such that the investigated samples are placed in the immediate vicinity of the reference sample as previously reported in [29,32]. This is specifically intended to avoid large variations in the local electromagnetic environment of measured samples.…”